After helping Norfolk capture the Calder Cup, on July 1, 2012, Kostka was signed as a free agent to a one-year contract by the Toronto Maple Leafs. Kostka got his first NHL point in his debut NHL game against the Montreal Canadiens on January 19, 2013.[4]

On July 19, 2013, Kostka signed as a free agent to a one-year, two way contract with the defending Stanley Cup champions, the Chicago Blackhawks.[5] He then scored his first NHL goal against the Leafs on October 19, 2013, against Jonathan Bernier. After only nine games with the Blackhawks and approaching the last quarter of the season, on February 23, 2014, Kostka was claimed off waivers by the Tampa Bay Lightning.[6]

After a successful stint with the Lightning, Kostka left as a free agent to sign a one-year contract with the New York Rangers on July 1, 2014.[7]